The K -Theory of Toric Schemes Over Regular Rings of Mixed Characteristic

@article{Cortias2017TheK,
  title={The K -Theory of Toric Schemes Over Regular Rings of Mixed Characteristic},
  author={Guillermo Corti{\~n}as and Christian Haesemeyer and Mark E. Walker and Charles Weibel},
  journal={arXiv: K-Theory and Homology},
  year={2017},
  pages={455-479}
}
We show that if X is a toric scheme over a regular commutative ring k then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was previously known for regular commutative rings containing a field. The affine case of our result was conjectured by Gubeladze. We prove analogous results when k is replaced by an appropriate K-regular, not necessarily commutative k-algebra. 
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